SOLUTION: Please help me solve this equation: {{{ 2x^2+3x-2=0 }}}

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Question 172185: Please help me solve this equation: +2x%5E2%2B3x-2=0+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2%2B3x-2=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=3, and c=-2


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%283%29+%2B-+sqrt%28+%283%29%5E2-4%282%29%28-2%29+%29%29%2F%282%282%29%29 Plug in a=2, b=3, and c=-2


x+=+%28-3+%2B-+sqrt%28+9-4%282%29%28-2%29+%29%29%2F%282%282%29%29 Square 3 to get 9.


x+=+%28-3+%2B-+sqrt%28+9--16+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-2%29 to get -16


x+=+%28-3+%2B-+sqrt%28+9%2B16+%29%29%2F%282%282%29%29 Rewrite sqrt%289--16%29 as sqrt%289%2B16%29


x+=+%28-3+%2B-+sqrt%28+25+%29%29%2F%282%282%29%29 Add 9 to 16 to get 25


x+=+%28-3+%2B-+sqrt%28+25+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-3+%2B-+5%29%2F%284%29 Take the square root of 25 to get 5.


x+=+%28-3+%2B+5%29%2F%284%29 or x+=+%28-3+-+5%29%2F%284%29 Break up the expression.


x+=+%282%29%2F%284%29 or x+=++%28-8%29%2F%284%29 Combine like terms.


x+=+1%2F2 or x+=+-2 Simplify.


So the answers are x+=+1%2F2 or x+=+-2